I have just installed Steam on my 64-bit Ubuntu 13.10 and it works well and I can play games, but each time I launch it I get the following prompt:
Steam needs to install these additional packages: 
    libgl1-mesa-dri:i386, libgl1-mesa-glx:i386
[sudo] password for user: 
............................................................................................................................................
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
 libgl1-mesa-dri:i386 : Depends: libdrm-intel1:i386 (>= 2.4.38) but it is not going to be installed
                        Depends: libdrm-nouveau2:i386 (>= 2.4.38) but it is not going to be installed
                        Depends: libdrm-radeon1:i386 (>= 2.4.31) but it is not going to be installed
                        Depends: libdrm2:i386 (>= 2.4.38) but it is not going to be installed
                        Depends: libglapi-mesa:i386 but it is not going to be installed
 libgl1-mesa-glx:i386 : Depends: libdrm2:i386 (>= 2.3.1) but it is not going to be installed
                        Depends: libglapi-mesa:i386 (= 9.2.1-1ubuntu3) but it is not going to be installed
                        Depends: libx11-6:i386 (>= 2:1.4.99.1) but it is not going to be installed
                        Depends: libxcb-dri2-0:i386 (>= 1.8) but it is not going to be installed
                        Depends: libxcb-glx0:i386 (>= 1.8) but it is not going to be installed
                        Depends: libxcb1:i386 but it is not going to be installed
                        Depends: libxdamage1:i386 (>= 1:1.1) but it is not going to be installed
                        Depends: libxext6:i386 but it is not going to be installed
                        Depends: libxfixes3:i386 but it is not going to be installed
                        Depends: libxxf86vm1:i386 but it is not going to be installed
E: Unable to correct problems, you have held broken packages.
Press return to continue: 
I have done the following :
sudo dpkg --add-architecture i386
sudo apt-get update
But no change whatsoever.
$ apt-cache policy libgl1-mesa-dri:i386 libgl1-mesa-glx:i386
libgl1-mesa-dri:i386:
  Installed: (none)
  Candidate: 9.2.1-1ubuntu3
  Version table:
     9.2.1-1ubuntu3 0
        500 http://archive.ubuntu.com/ubuntu/ saucy/main i386 Packages
libgl1-mesa-glx:i386:
  Installed: (none)
  Candidate: 9.2.1-1ubuntu3
  Version table:
     9.2.1-1ubuntu3 0
        500 http://archive.ubuntu.com/ubuntu/ saucy/main i386 Packages
$ sudo apt-get check
Reading package lists... Done
Building dependency tree       
Reading state information... Done
after sudo apt-get install aptitude && sudo aptitude install libgl1-mesa-dri:i386 libgl1-mesa-glx:i386 
The following NEW packages will be installed:
  libdrm-intel1:i386{ab} libdrm-nouveau2:i386{ab} libdrm-radeon1:i386{ab} libdrm2:i386{ab} libelf1:i386{a} libexpat1:i386{a} libffi6:i386{a} libgl1-mesa-dri:i386{b} 
  libgl1-mesa-glx:i386{b} libglapi-mesa:i386{ab} libllvm3.3:i386{a} libpciaccess0:i386{a} libtxc-dxtn-s2tc0:i386{a} libx11-6:i386{a} libx11-xcb1:i386{a} libxau6:i386{a} 
  libxcb-dri2-0:i386{ab} libxcb-glx0:i386{ab} libxcb1:i386{ab} libxdamage1:i386{a} libxdmcp6:i386{a} libxext6:i386{a} libxfixes3:i386{a} libxxf86vm1:i386{a} zlib1g:i386{a} 
0 packages upgraded, 25 newly installed, 0 to remove and 0 not upgraded.
Need to get 13,8 MB of archives. After unpacking 45,0 MB will be used.
The following packages have unmet dependencies:
 libxcb-dri2-0 : Breaks: libxcb-dri2-0:i386 (!= 1.10-1~xedgers~saucy1) but 1.9.1-3ubuntu1 is to be installed.
 libxcb-dri2-0:i386 : Breaks: libxcb-dri2-0 (!= 1.9.1-3ubuntu1) but 1.10-1~xedgers~saucy1 is installed.
 libdrm-intel1 : Breaks: libdrm-intel1:i386 (!= 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy) but 2.4.46-1ubuntu1 is to be installed.
 libdrm-intel1:i386 : Breaks: libdrm-intel1 (!= 2.4.46-1ubuntu1) but 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy is installed.
 libgl1-mesa-dri : Breaks: libgl1-mesa-dri:i386 (!= 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy) but 9.2.1-1ubuntu3 is to be installed.
 libgl1-mesa-dri:i386 : Breaks: libgl1-mesa-dri (!= 9.2.1-1ubuntu3) but 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy is installed.
 libdrm-radeon1 : Breaks: libdrm-radeon1:i386 (!= 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy) but 2.4.46-1ubuntu1 is to be installed.
 libdrm-radeon1:i386 : Breaks: libdrm-radeon1 (!= 2.4.46-1ubuntu1) but 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy is installed.
 libxcb1 : Breaks: libxcb1:i386 (!= 1.10-1~xedgers~saucy1) but 1.9.1-3ubuntu1 is to be installed.
 libxcb1:i386 : Breaks: libxcb1 (!= 1.9.1-3ubuntu1) but 1.10-1~xedgers~saucy1 is installed.
 libglapi-mesa : Breaks: libglapi-mesa:i386 (!= 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy) but 9.2.1-1ubuntu3 is to be installed.
 libglapi-mesa:i386 : Breaks: libglapi-mesa (!= 9.2.1-1ubuntu3) but 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy is installed.
 libxcb-glx0 : Breaks: libxcb-glx0:i386 (!= 1.10-1~xedgers~saucy1) but 1.9.1-3ubuntu1 is to be installed.
 libxcb-glx0:i386 : Breaks: libxcb-glx0 (!= 1.9.1-3ubuntu1) but 1.10-1~xedgers~saucy1 is installed.
 libgl1-mesa-glx : Breaks: libgl1-mesa-glx:i386 (!= 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy) but 9.2.1-1ubuntu3 is to be installed.
 libgl1-mesa-glx:i386 : Breaks: libgl1-mesa-glx (!= 9.2.1-1ubuntu3) but 10.1.0~git20140102.5a51c1b0-0ubuntu0ricotz~saucy is installed.
 libdrm-nouveau2 : Breaks: libdrm-nouveau2:i386 (!= 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy) but 2.4.46-1ubuntu1 is to be installed.
 libdrm-nouveau2:i386 : Breaks: libdrm-nouveau2 (!= 2.4.46-1ubuntu1) but 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy is installed.
 libdrm2 : Breaks: libdrm2:i386 (!= 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy) but 2.4.46-1ubuntu1 is to be installed.
 libdrm2:i386 : Breaks: libdrm2 (!= 2.4.46-1ubuntu1) but 2.4.50+git20140102.e8cbc579-0ubuntu0ricotz~saucy is installed.
The following actions will resolve these dependencies:
      Remove the following packages:                                                        
1)      gir1.2-totem-1.0                                                                    
2)      gnome-contacts                                                                      
3)      gnome-control-center                                                                
4)      gnome-control-center-datetime                                                       
5)      gnome-control-center-signon                                                         
6)      gnome-control-center-unity                                                          
7)      gstreamer1.0-clutter                                                                
8)      gstreamer1.0-plugins-bad                                                            
9)      indicator-bluetooth                                                                 
10)     libcheese-gtk23                                                                     
11)     libcheese7                                                                          
12)     libclutter-1.0-0                                                                    
13)     libclutter-gst-2.0-0                                                                
14)     libclutter-gtk-1.0-0                                                                
15)     libcogl-pango12                                                                     
16)     libcogl12                                                                           
17)     libegl1-mesa                                                                        
18)     libegl1-mesa-drivers                                                                
19)     libgbm1                                                                             
20)     libgl1-mesa-dri                                                                     
21)     libgstreamer-plugins-bad1.0-0                                                       
22)     libtotem0                                                                           
23)     libxatracker1                                                                       
24)     ubuntu-desktop                                                                      
25)     xorg                                                                                
26)     xserver-xorg-glamoregl                                                              
27)     xserver-xorg-video-all                                                              
28)     xserver-xorg-video-vmware                                                           
      Keep the following packages at their current version:                                 
29)     libdrm-intel1:i386 [Not Installed]                                                  
30)     libdrm-nouveau2:i386 [Not Installed]                                                
31)     libdrm-radeon1:i386 [Not Installed]                                                 
32)     libdrm2:i386 [Not Installed]                                                        
33)     libgl1-mesa-dri:i386 [Not Installed]                                                
34)     libgl1-mesa-glx:i386 [Not Installed]                                                
35)     libglapi-mesa:i386 [Not Installed]                                                  
36)     libx11-6:i386 [Not Installed]                                                       
37)     libxcb-dri2-0:i386 [Not Installed]                                                  
38)     libxcb-glx0:i386 [Not Installed]                                                    
39)     libxcb1:i386 [Not Installed]                                                        
40)     libxdamage1:i386 [Not Installed]                                                    
41)     libxext6:i386 [Not Installed]                                                       
42)     libxfixes3:i386 [Not Installed]                                                     
43)     libxxf86vm1:i386 [Not Installed]                                                    
      Leave the following dependencies unresolved:                                          
44)     gnome-bluetooth recommends gnome-control-center                                     
45)     indicator-power recommends gnome-control-center (>= 3.1) | ubuntu-system-settings   
46)     indicator-sound recommends gnome-control-center | ubuntu-system-settings            
47)     libaccount-plugin-1.0-0 recommends gnome-control-center-signon                      
48)     unity recommends gnome-control-center-unity                                         
49)     unity recommends indicator-bluetooth                                                
50)     xserver-xorg recommends libgl1-mesa-dri                                             
51)     ubuntu-restricted-addons recommends gstreamer1.0-plugins-bad                        
52)     gnome-control-center-data recommends gnome-control-center (>= 1:3.6.3-0ubuntu45.2)  
53)     indicator-datetime recommends gnome-control-center-datetime | ubuntu-system-settings
54)     xserver-xorg-core recommends libgl1-mesa-dri (>= 7.10.2-4)                          
55)     libgl1-mesa-glx recommends libgl1-mesa-dri (>= 7.2)                                 
56)     xserver-xorg-video-nouveau recommends libgl1-mesa-dri (>= 7.11.1)                   
57)     libegl1-mesa recommends libegl1-mesa-drivers                                        
Accept this solution? [Y/n/q/?] 
Those are my additionally installed PPAs:
./danielrichter2007-grub-customizer-saucy.list
./danielrichter2007-grub-customizer-saucy.list.save
./dropbox.list
./dropbox.list.save
./google-chrome.list
./google-chrome.list.save
./linrunner-tlp-saucy.list
./linrunner-tlp-saucy.list.save
./me-davidsansome-clementine-saucy.list
./me-davidsansome-clementine-saucy.list.save
./steam.list
./steam.list.save
./webupd8team-java-saucy.list
./webupd8team-java-saucy.list.save
 
     
     
     
     
     
     
     
    